which can be computed via conformal field theory techniques (see also [1]}, [2]}).
To appreciate the structure of Eq. (REF ), we take for exampleOther choices of \(n^{1}_{N}\)  and \(n^{2}_{N}\)  will yield more complex expressions,
but similar physics.
\(n^{1}_{N}=2,~ n^{2}_{N}=1\) . They are shown by three simple
triangles in figure 1.
Non-perturbative terms in each torus are proportional to
\(\left(H^{ij}_{u}\lambda _{a}^{i}\bar{\lambda }_{b}^{j}e^{-\mathcal {A}_{1}}+H^{ij}_{d}\lambda _{a}^{i}\bar{\lambda }_{b}^{j}e^{-\mathcal {A}_{1}}\right)&+&\left(H^{ij}_{u}\lambda _{a}^{i}\bar{\lambda }_{b}^{j}e^{-\mathcal {A}_{2}}+H^{ij}_{d}\lambda _{a}^{i}\bar{\lambda }_{b}^{j}e^{-\mathcal {A}_{2}}\right),\nonumber \\H^{ij}_{u}\lambda _{a}^{i}\bar{\lambda }_{b}^{j}e^{-\mathcal {A}_{3}}&+&H^{ij}_{d}\lambda _{a}^{i}\bar{\lambda }_{b}^{j}e^{-\mathcal {A}_{3}},\nonumber \\H^{ij}_{u}\lambda _{a}^{i}\bar{\lambda }_{b}^{j}e^{-\mathcal {A}_{4}}&+&H^{ij}_{d}\lambda _{a}^{i}\bar{\lambda }_{b}^{j}e^{-\mathcal {A}_{4}},\) 
